Various Measures of Yields - Essay Example

Economics: Banking & Finance Assignment 2 Student Name Registration Number Course Year of Study Instructor Economics: Banking & Finance- Assignment 2 The bond yield measure sensitizes investors of the interest rate on bonds given different scenarios. This essay describes the different measures of bond yield giving practical examples and also explains how changes in interest rates could influence the bond prices. The bond yield The term bond yield also known as the rate of interest refers to the percentage return received by the investor after issuing a bond of a given maturity date (Ho and Lee, 1986, p. 1011-1015). However, computation of interest rate uses the current data bearing the current bond price rather than the price at which it was purchased. Nonetheless, determination of the current bond price also demands a clear understanding of the prevailing interest rate for a given security. Essentially, the determination of the bond rate of return requires the buyer to hold on the bond for an extended period of time. The main types of bond yields The yield computed is also known as the internal rate of return. Below are the most common types of bond yields; Coupon rate Coupon rate refers to the interest rate carried by a given bond and one that is payable to the investor on maturity. For example, a bond that bears an interest rate of 5% means that, an investor who purchases a bond prior to prices fluctuations should expect an a similar annual interest rate during the foreseeable life of that particular bond prior to adjusting for the issue costs. In other words, the investors should understand that coupon rate is the same as the interest rate. Running yield The running yield refers to the interest rate that prevails in the secondary market for the trading bonds. Basically, in the secondary market, the bond prices keep on fluctuating and so does their interest rate. Redemption yield The redemption yield refers to the interest rate on the face value or nominal value of bonds that bears a fixed life span. Different measures of bond yield The bond interest rates can be measured through either of the following methods; the nominal yield, current yield, yield to call, yield to maturity or the realized or horizon yield. Nominal yield This entails the interest rate of a given bond based on the issue or nominal price. For instance, a bond issued with a coupon of 8% carries a nominal yield of 8%. Current yield The current yield involves the market price of the cash inflows and the nominal value of the bond. However, the current yield has one main limitation as it fails to take into consideration the time value of money. In addition, it also fails to accommodate any other source of return such as capital gains into consideration in arriving at the security return. Nonetheless, it is one of the easiest ways to compute the bond interest rate arrived to as follows; Current yield= Interest rate/ prevailing market price x 100 For instance; given a market price of $ 120 for 8% municipal bond, the current yield should be computed as follows; 8/120x 100 = 6.7% Yield to maturity (YTM) Yield to maturity is one of the widely known measures of bond interest rate. It is also commonly known as internal rate of return meaning the return that the investor anticipates after holding the bond to maturity. However, despite being the most re-known measure, there are few limitations such as, the assumption that the interest rate is paid all along the entire life of the bond, and the other assumption is that the interest earned is re-invested at similar interest rate (Hull and White, 1990, p. 573-292). Usually, bond interest rates are payable twice a year and investors are assumed to automatically re-invest the interest received. The yield to maturity method takes into account the time value of money by incorporating the timing of the cash flows together with the related potential capital gains that would accrue to investors who holds the bond to maturity. Unfortunately, the re-investment rate may not be equal to Year to Maturity rate hence the greatest set-back of the year to Maturity yield determination method. The YTM is determined as follows; The relationship that exists amongst the coupon rate, current yield and yield to maturity is given as follows; Bond Market Price The relationship expected Par Coupon rate= Current yield = Yield to Maturity Discount Coupon rate < Current yield < Yield to Maturity Premium Coupon rate > Current yield > Yield to Maturity The yield to maturity holds the assumption that the bond investment is held by the investor to its maturity date, and all the interim cash flows are reinvested at the prevailing interest rate as all the cash flows are traded at that particular rate. It is, therefore, imminent for investors to note that, the re-investment assumption of the actual return varies with the term to maturity and bond interest rate. Notably, a higher interest rate and the corresponding extended term to maturity increase the bond loss in value as a result of failure to re-invest at the interest to maturity terms. As such, the higher coupon rate coupled with a longer maturity period makes the re-investment assumption highly esteemed. Illustration Given a bond bearing an annual interest rate of 15% that is redeemable after a period of three years selling at $ 90.00. Calculate the interest rate, earned by the investor who purchased the bond and holds it to maturity. Present value- $ 90.00 Coupon rate- 15% Number of years- 3 years Future value- $ 100.00 (Assumed that the bond is redeemed at its face value) The return (I/Y) = 14.33% Yield to call (TYC) This is the interest receivable if one acquires a callable bond that matures when the issuer decides to redeem it, usually prior to the maturity date. Yield to call equates the bond price to the current rate of the cash flows up to the initial call date with the assumption that the bond in question is retained till the first call date. Nonetheless, the computation of the yield call is pretty similar to that of Yield to Maturity. Investors have a choice to select between yield to maturity and yield to call as a measure of bond return by considering the lower of the two as their preferred measure of return. Similar to yield to maturity, the yield to call also assumes that the re-investment of the interim cash flows is at the yield to call rate. Also, it assumes that the bond is held to its first call date. Horizon Yield This measure gives the expected rate of return that an investor expects from selling the bond prior to its maturity. In short, it is an interest measure that enables the investor to forecast the probable performance of the bond on the basis of the planned investment horizon the expectations concerning the re-investment rates and the future market yields. Further, this measure allows the investor to evaluate which of the numerous bonds should be considered for investment after consideration of the favorable performance over the investment period. Basically, the use of total return to determine the bond performance over a given investment horizon is referred to as horizon analysis while the calculated return over the same horizon is known as the horizon return or yield. However, the limitation of this approach is that it requires the investor to make some assumptions in regard to reinvestment rates, too think in terms of the horizon and the future yields. Nonetheless, it enables the investor to determine the bond performance under varied interest rate scenarios hence the ability to assess the sensitivity of the bond to interest rate variations. The relationship between interest rate changes and bond prices A decrease in bond interest rate calls for increase in the term of the bond in order to experience maximum bond prices. An increase (decrease) in the bond Return leads to the corresponding decrease (increase) in the price of the bond. The following is a graphical representation of the relationship that exist between price and bond yield. Figure-1 Price Yield Notably, the shape of the price-yield relationship is convex. The rate of change in the bond price is measured as a percentage of change in bond price. However, besides changes in interest rate behavior, the price of the bond is influenced by other factor such as the par value. Based on figure one above, it is necessary to note the following relationships that exist between the bond price and the interest rate behavior; the price moves in a negative relationship to bond interest rate, for every change in bond interest, the maturing bond bears a different price hence the bond price volatility is directly related to term of maturity. Additionally, the price unpredictability increases at a decreasing rate as the term to maturity increases. More so, the price changes occasioned by the absolute changes in interest rate do not remain unchanged as a rate of decrease in yield widens. Rather, the bond price changes by more than the increase in interest of a similar amount that lowers the bond prices. Lastly, for a given change in bond return, the higher interest leads to a smaller percentage fluctuation. That is price fluctuations have an inverse relationship to the rate of return. Referring to the figure above, the convexity of the curve is useful for investors in comparison of different securities. In this regard, if two bonds offer the same duration of time and interest rate and one exhibits greater convexity, then the change in interest rates will cause changes on each bond differently (Vasicek, 1977, p.178-178). Basically, the interest rate changes have minimal effect on the bond with greater convexity compared to that with lesser convexity. More importantly, bonds with greater convexity bear higher prices as compared to those with lesser convexity irrespective of the variations in the interest rates. This relationship is illustrated in the following diagram: Figure-2 As seen from the above diagram, bond A has a more convex curve compared to bond B, despite the similarity in both prices as shown by price *P and yield *Y. If the interest rate changes from this equilibrium point by a small margin, then the two bonds will bear same prices irrespective of the convexity of their curves. On the other hand, when rate of return increases by a significant amount, both prices of bond A and B decreases, but the price of bond B will decrease more than that of bond A. At **Y, the price of bond A remains high indicating that investors will part with extra money, leading to lower returns on bond maturity. According to Campbell (1989, p. 38-45), callable bonds have negative convexity at any given price-yield relationship. The adverse convexity indicates that, the market return decreases as the duration to maturity decreases. As the bond return increases, the price decreases resulting to rise in interest rates. At this point, it would be cost effective or exceeding optimal for the bond issuer to call it as the interest rates will have decreased below the callable bonds interest rate. Further decrease in bond yield below the equilibrium point leads to more negative convexity, which could cause greater risk for the bond issuer, were he to call the bond. In this regard, the bond return below the equilibrium point for a callable bond will not rise as prices rise. Therefore, for any given bond the graphical relationship between the bond price and the yield is convex meaning that the graph forms a curve instead of a straight line. However, the extent to which the graph is curved indicates how the bond in return changes, in response to price change, as occasioned by changes in interest rates. Figure-3 As indicated on figure 3 above, as the bond return moves further away from the equilibrium point, Y*, the part colored in yellow between the estimated and actual bond price increases. In this light, the convexity calculation helps the investor to estimate the inaccuracies of placing his investment in bonds market. More importantly, the convexity helps the investor to estimate the possible change in bond price as the volatile interest rate keeps on changing. References Campbell, R. H. (1989). Forecasting Economic Growth with the Bond and Stock Markets, Financial Analysts Journal, 9.3, 38-45. Ho, T. and Lee, S.B. (1986). Term Structure Movements and Pricing Interest Rate Contingent Claims. Journal of Finance, 4.1, 1011- 1029. Hull, J. and White, A. (1990). Pricing Interest-Rate-Derivative Securities. The Review of Financial Studies, 3.2, 573-92. Vasicek, O. A. (1977). An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, 5.7, 177-88. Read More